研究目的
To present a new approach for solving the Abel integral equation in analyzing the laser-induced breakdown spectroscopy (LIBS) that is singularity free and derivative free, suitable for dealing with LIBS problem for any form of the measured intensity and insensitive to noisy intensity data.
研究成果
The proposed method is both derivative free and singularity free, easy to handle, and insensitive to noisy data measured. It can construct the emissivity from any given intensity. The efficiency and accuracy of the method are demonstrated by two examples.
研究不足
The paper does not explicitly mention limitations of the research.
1：Experimental Design and Method Selection:
A collocation method is applied to solve the Abel integral equation. The Abel integral equation is transformed to a singularity free and derivative free integral equation. The solution of the integral equation is expanded to a polynomial of degree n, approximated by a linear system established by the collocation method.
2：Sample Selection and Data Sources:
Simulated experimental data with or without noise is used as input for the method.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned in the paper.
4：Experimental Procedures and Operational Workflow:
The method involves transforming the Abel integral equation, expanding the solution to a polynomial, and solving a linear system to approximate the solution.
5：Data Analysis Methods:
The accuracy of the results is evaluated using the root-mean-square (RMS) error.
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